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 PDE Seminar

For further information, or to suggest a PDE Seminar speaker, please contact:

Misha Perepelitsa Gabriela Jaramillo William Fitzgibbon


Click Here for prior year seminars

Seminar on Partial Differential Equations
Fall 2021

All talks in ZOOM, Friday at 2:00 PM
Click here for Fall 2019

September 3
September 10  
 September 17  
September 24  
October 1  
October 8 Dr Benedetto Piccoli (Rutgers U)

PDE models for vehicular traffic and smoothing via autonomous vehicles
PDE models are used since the 60s to deal with traffic flow. In the 90s a theory of conservation laws on graphs was proposed for road networks, and more recently models included ODE-PDE systems, phase transitions, and mean-field. We present a general view on the use of PDE models in traffic, then turn to recent applications

October 15

October 22  
October 29  
November 5  
November 12 Dr Elena Camacho Aguilar (Rice U)

Title: Formalizing the Waddington landscape metaphor using Catastrophe Theory
During the development of an organism, cells specialize by transitioning between a limited set of discrete cell fates, each defined by a distinct gene expression profile. These transitions occur in a characteristic sequence and are controlled by cues in the environment, such as the presence of morphogens or signals. While quantitative models that describe signaling pathways and gene regulatory networks in great detail have been used to investigate cell differentiation, these suffer from having too many parameters to constrain with available data. Furthermore, their complexity makes it difficult to gain intuitive understanding or to make predictions without case-by-case simulation. A popular and intuitive metaphor for the process of cell differentiation is the Waddington landscape, in which a differentiating cell is represented as a marble rolling down a landscape of hills and valleys, encountering decision points between different lineages, eventually settling in a valley that defines its cell fate. We show that this metaphor can be mathematically formalized using Catastrophe Theory, where the landscape is defined by a potential function and the different cell states correspond to attractors in the landscape. In this setting, variation in the parameters of the dynamical system, caused by changes in the signals the cell receives, alter the landscape and give rise to bifurcations that destroy or create attractors. Moreover, by combining this approach with approximate Bayesian computation, we show that we can quantitatively fit these models to large amounts of biological data and make novel predictions. In this talk, I will show how we took advantage of this formalism to model vulval development in C. elegans as well as murine trunk development, allowing us to deeply understand the underlying cell state transitions and to make numerous predictions of untested experimental conditions.
November 19 Dr Konstantinos Spiliopoulos (Boston U)

November 26  
December 3  

Small changes/shifts in the dates may be possible.

   University of Houston